Relations between the US and Russia appear to have reached depths not seen since the end of the Cold War.

The country's top two diplomats have admitted that there is little trust between them.

Moments after the US secretary of state Rex Tillerson and Russia's foreign minister Sergei Lavrov ended a news conference in Moscow, Russia vetoed the latest UN resolution condemning the reported use of chemical weapons in Syria.

Donald Trump went on to describe US relations with Russia as at an "all-time low", and Russian president Vladimir Putin said the "level of trust" had "not improved but has rather deteriorated".

During his visit to Moscow on Wednesday, Mr Tillerson said US-Russia ties had reached a "low point" - despite a lengthy meeting with Mr Putin and Mr Lavrov.

"The world's two foremost nuclear powers cannot have this type of relationship," Mr Tillerson warned.

Video:Tillerson: US-Russia trust at 'low level'

He restated America's claim that Syrian government forces "planned, directed and executed" a chemical attack on civilians which killed more than 80 people.

Mr Tillerson said the Trump administration's position was clear: Bashar al Assad has to relinquish the presidency.

"Russia, as their closest ally in the conflict, perhaps has the best means of helping Assad recognise this reality," he told reporters.

On Thursday, a Kremlin spokesman said the discussions between Mr Tillerson and Mr Putin had been "fairly constructive", and that the president used the meeting to explain why ties were at such a low point - while they had agreed to keep lines of communication open.

Both Syria and Russia have denied that forces loyal to the Assad regime carried out the toxic gas attack in the town of Khan Sheikhoun on 4 April. Moscow has blamed Syrian rebels.

Mr Lavrov denounced America's missile strikes on a Syrian airbase, launched in the aftermath of the attack, as illegal and accused Washington of behaving unpredictably.

One of his deputies went further, telling Russia's state-owned news agency: "In general, primitiveness and loutishness are very characteristic of the current rhetoric coming out of Washington."

Video:Putin: US planning strikes on Damascus

UK analysis of samples from the scene has detected sarin or a sarin-like substance.

Mr Trump's pre-election calls for closer ties with Russia and Mr Putin seem to have been overtaken by their differences over the war in Syria.

Mr Lavrov admitted relations between the two nations "are not the most calm" and some issues were "time bombs" inherited from the Obama administration.

But he said Moscow and Washington had agreed to continue co-operating to try to find a political solution for Syria.

The Russian diplomat claimed some progress was made on the crisis in the war-ravaged country and a working group would be set up to examine the poor state of US-Russia relations.

Video:Trump: NATO 'no longer obsolete'

Meanwhile, Mr Trump has also declared NATO is "no longer obsolete" - and has said he is committed to the military alliance.

Before taking office in January, Mr Trump questioned the relevance of the organisation, which was created after World War Two.

He had said it was "obsolete because it was designed many, many years ago".

But in an apparent reversal, Mr Trump said the alliance is a "bulwark of international peace and security".